Accelerating distributed consensus using extrapolation

In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature attack this problem by distributed linear iterative algorithms, with asymptotic convergence of the consensus solution. In this letter, we propose the use of extrapolation methods in order to accelerate distributed linear iterations. The extrapolation methods are guaranteed to converge in a finite number of steps, upper bounded by the number of sensors. In particular, we show that the Scalar Epsilon Algorithm (SEA) can accelerate vector sequences produced by distributed linear iterations, with no communication overhead and without knowledge of the full network topology. We provide simulation results that demonstrate the validity and effectiveness of the proposed scheme.